A new measurement of the neutron EDM, using Ramseys method of separated oscillatory fields, is in preparation at the new high intensity source of ultra-cold neutrons (UCN) at the Paul Scherrer Institute, Villigen, Switzerland (PSI). The existence of a non-zero nEDM would violate both parity and time reversal symmetry and, given the CPT theorem, might lead to a discovery of new CP violating mechanisms. Already the current upper limit for the nEDM (|d_n|<2.9E-26 e.cm) constrains some extensions of the Standard Model. The new experiment aims at a two orders of magnitude reduction of the experimental uncertainty, to be achieved mainly by (1) the higher UCN flux provided by the new PSI source, (2) better magnetic field control with improved magnetometry and (3) a double chamber configuration with opposite electric field directions. The first stage of the experiment will use an upgrade of the RAL/Sussex/ILL groups apparatus (which has produced the current best result) moved from Institut Laue-Langevin to PSI. The final accuracy will be achieved in a further step with a new spectrometer, presently in the design phase.